To get a handle of the economy just remember that Qatar has a 5:1 (1.5M/300K) guest worker/slave to citizen ratio. Qatar is an example of what happens when a group of people get more money than they know what to do, and then they figure out what to do with it.This is why IMHO, like all news, the Al Jazeera news network should be taken with as much salt as the western state or business backed news networks.It doesn't help that too much of the philanthropy ends up supporting very off the wall Suni extremism outside Qatar.Not to mention the escaped guest worker(slave) laws and right to block worker exit from Qatar.
en.wikipedia.org

Qatar (/ˈkæˌtɑr/, i/ˈkɑːtɑr/, /ˈkɑːtər/ or i/kəˈtɑr/; Arabic: قطر‎ Qaṭar [ˈqɑtˤɑr]; local vernacular pronunciation: [ɡɪtˤɑr]), officially the State of Qatar (Arabic: دولة قطر‎ Dawlat Qaṭar), is a sovereign country located in Southwest Asia, occupying the small Qatar Peninsula on the northeastern coast of the Arabian Peninsula. Its sole land border is with Saudi Arabia to the south, with the rest of its territory surrounded by the Persian Gulf. A strait in the Persian Gulf separates Q Following Ot...

Ski Dubai is an indoor ski resort with 22,500 square meters of indoor ski area. It is a part of the Mall of the Emirates, one of the largest shopping malls in the world, located in Dubai, United Arab Emirates. It was developed by Majid Al Futtaim Group, which also operates the Mall of the Emirates. Opened in November 2005, the indoor resort features an 85-meter-high indoor mountain with 5 slopes of varying steepness and difficulty, including a 400-metre-long run, the world's first indoor black ru...

I don't understand why Qatar has (or seems to have) its foreign policy fingers in certain pies. I recall reading that the Islamists in the Malian rebellion were supported by Qatar, though that was in one news article and I haven't since seen that assertion. Now, over the weekend, there was a battle at the airport in Tripoli; the anti-Islamists are supposedly helped by the UAE and Egypt while the Islamists are backed by Qatar.

If Qatar is doing this, I don't get it. They don't maintain that kind of fundamentalism at home so I can't understand why they'd support it elsewhere. Maybe it has nothing to do with the philosophy and it's a means to some other end -- but what, and why?

I understand that Saudi Arabia exports it's radicals and funds them to keep the jihad at arms length, probably the same thing with Qatar. Kicking the can down the road hoping to run the clock down until it is someone else's problem IMHO.